5 Second order linear regression Trust Flow vs. Domain Authority

Majestic Trust Flow or Moz Domain Authority for SEO?

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In Search Engine Optimisation (SEO), you often want to know how strong a website is. Two different metrics that attempt to measure this are Domain Authority (DA) from Moz and Trust Flow (TF) from Majestic

Both Trust flow and Domain Authority help SEO professionals make judgements about the usefulness of backlinks from a site in order to ensure their website ranks higher in Google (and other search engines).

What I’ve been wondering is: do they measure the same thing? That’s what we will find out in this report.

Why?

If the two metrics measure the same thing (they correlate), it would suggest two things:

First, you can translate one into other. This can be useful in practice when for example when you want to compare sites but don’t have all the data.

Second, if two metrics correlate, this suggests the are probably both pretty good metrics . Because what are the odds that two companies independently both get it wrong in the same way?

However, if the metrics are not similar (when there is little correlation between them), it would seem that at least one of them must must be wrong.

Last year, we already concluded that Trust Flow is a good predictor of organic search engine traffic to a domain. This is an indication that is is a good metric for estimating the strength of a domain  from a search engine perspective.

How?

To analyse the similarity  I first collected the Domain Authority and Trust flow for a sample of 2309 domains. The sample was created from domains that that rank on Google.co.uk for keywords related to celebrity gossip and showbiz news. 

Note that the topic of the domains is not relevant to the conclusion of the study. It is expected generalise to all websites, regardless of their category.

To analyse the data, I used linear regression. This statistical method enables me to estimate the relationship between Domain Authority and Trust Flow. It also lets me determine correlation bewteen the metrics, which is a meassure of the strength of this relationship.

The Data

Before we start, I want to get to know the data a bit better. Below are two charts, one for Trust Flow and one for Domain Authority, that shows the 2309 domains and how they are distributed over the values of the respective metrics. Each x axis is divided it bars of 10. On the Y axis is the count of domains in that group.

We can see that metrics have more low quality than high quality domains. However where Majestic has most of its sites under Trust Flow 30. Domain authority has most between 10 and 40.

Trust flow’s higher value domains gradually reduce in quantity as the Trust Flow increases. Domain Counts for Domain Authority’s higher values stay constant up to DA 100.

 

1 Majestic histogram 2 Moz histogram

 

Regression analysis

We want to understand how Trust Flow and Domain Authority are related, and how strong the relationship is. Both goals are achieved through regression analysis. This means that we let the computer draw the best fitting line through the points in the charts below. How well this line fits the points determines the strength of the relationship (correlation). This can be expressed as the correlation coefficient R^{2}.

Regression 1

In the chart below, every black dot represents one of the 2309 domains analysed, with their Trust Flow value on the Y axis, and Domain Authority on the X axis. The thin blue line is the average Trust Flow at the corresponding level of Domain Authority. The red line is the best fit for the first order relationship between Trust Flow and Domain Authority. A first order relationship means that it is a formula in the form:

y = a + bx

 

Were a and b are the coefficients to be found by the regression analysis. 

3 First order linear regression Trust Flow vs. Domain Authority

 

The analysis shows that the relationship between TF and DA is:

TF = -7.92 + 0.78 * DA

 

The correlation for this formula is:

R^{2} = 0.8023

 

This is a very high number that suggests that Trust Flow and Domain Authority can are related. Specifically, more than 80% of the value of Trust Flow can be explained when you know the Domain Authority of a website and the other way round.

 

Residuals 1

We can learn more about the relationship between TF and DA by analysis the residuals of the regression model. The residuals are the difference between the real values, and the values predicted by the formula calculated in the regression analysis. The residuals (difference) of Trust Flow are plotted on the y axis against the predicted  Trust Flow on the x axis. The blue line is the smoothed average at the corresponding Trust Flow value

.4 First order linear regression Residials vs. Predicted Trust Flow

 

 

In a well-fitting model the residuals are equally distributed above and below the y = 0 line for all values of the x axis. In this chart that is mostly true. However, in the low and high values of the prediction, the line goes up. This means it that appears the model underestimates the actual Trust Flow when we know the Domain Authority. Maybe the model can be improved.

Regression 2

When we look at the first scatter plot, it seems that the dots follow a slightly curved trajectory. Therefore it may be appropriate to try a second order polynomial regression. This means we try to find a formula in the form:

y = a + bx + cx^{2}

 

The plot below shows the same dots as in the first chart, but now the red line represents this second order relationship.5 Second order linear regression Trust Flow vs. Domain Authority

 

In this case, the relationship can be expressed as follows:

TF = 3.134 + 0.215 * DA+ 0.054 * DA^{2}

 

The correlation for this formula is

R^{2} = 0.826

 

The correlation for this formula is slightly higher than the first order equation. Thus, this formula is better than the previous. We can also see this in the residuals plot below.

Residuals 2

6 Second order linear regression Residials vs. Predicted Trust Flow

 

This plot shows that in the lower levels of predicted Trust Flow, the relation is much better. In the higher values it’s still skewed upwards, though less than in the first order relationship.

Confidence intervals

Thus as analysed above, it appears that we can use the formula

TF = 3.134 + 0.215 * DA+ 0.054 * DA^{2}

 

To calculate Trust Flow from Domain Authority. A correlation of over 82% means that it is mostly correct, but as the residuals chart shows, in many cases the actual value is higher or lower than the predicted one. To get a better understanding of the relationship, we can calculate a confidence interval where 95% of the time, the actual Trust Flow value will fall inside.

The formulas for the upper and lower limits of the confidence intervals are as follows:

 

Conclusion

In this post I showed how we can translate the Moz Domain Authority into MajesticSEO Trust Flow. The relationship has a correlation coefficient   R^{2} of 0.82. This suggests that the two metrics are mostly measuring the same thing, and can thus be substituted for each other. We use the quadratic equation to map the DA to TF.

Because there is a spread in the results, it may be better to express the relationship as confidence intervals. The formulas for the 95% confidence interval have specified.

The practical meaning of this analysis has been to show that MajesticSEO and Moz mostly agree on their way of classifying authority of website. Moz is more generous than Majestic giving higher values, but this in itself doesn’t tell you which metric is better.

That’s because this analysis cannot tell us which of the metrics are more closely related to SEO performance. It does however instil confidence because two companies independently create proxies for PageRank that agree with each other. Hopefully this means they also agree with Google.

Appendix

For your convenience, I provided below a table that you can use to translate a Domain Authority of a site into the corresponding Trust Flow, and vice versa. The 95% confidence interval column gives the amount that you need to add or subtract to stay within the interval. Note that all values are rounded to the nearest integer. For example, a Domain Authority of 10 is 95% of the times equal to Trust Flow between 8 and 12.

Domain authority
Trustflow
Trustflow 95% confidence (up or down)
132
242
342
442
542
652
752
852
962
1062
1162
1262
1372
1472
1583
1683
1783
1893
1993
20103
21103
22103
23113
24113
25123
26124
27134
28134
29144
30144
31154
32164
33164
34174
35175
36185
37195
38195
39205
40205
41215
42225
43225
44236
45246
46256
47256
48266
49276
50276
51286
52297
53307
54317
55317
56327
57337
58347
59358
60368
61368
62378
63388
64398
65408
66419
67429
68439
69449
70459
71469
72479
734810
744910
755010
765110
775210
785310
795411
805511
815611
825711
835811
846011
856112
866212
876312
886412
896512
906713
916813
926913
937013
947113
957313
967414
977514
987614
997814
1007914
Summary
Article Name
Majestic Trust Flow or Moz Domain Authority for SEO?
Author
Description
How well do Moz Domain Authority and MajesticSEO Trustflow correlate? This article applies regression analysis to describe the relationship between them, so that you can convert one into the other.
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On February 24, 2014
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One Response to Majestic Trust Flow or Moz Domain Authority for SEO?

  1. Gillis,
    Thankyou for your work. I understand that Majestic & MOZ have their different metrics. It would be nice if we could have a single metric. Thanks for your attempt to bring some correlation between them. The SEO community definitely needs this. Nice report.

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